# vector analysis integrals

• Nov 29th 2007, 01:22 PM
universe09
vector analysis integrals
question.

if F(x,y) = f(x,y)i + g(x,y)j
f and g are continuous on an open connected region D.

a) what can you say about the work integrals of F along paths in D if
F = del(phi ), for some function phi(x,y)?

b) what can you say about F and work integral of F along paths in D if fsuby=gsubx throughout D?
What assumptions must be made about D?

C) given F(x,y) = (e^y +ye^x )i +(xe^y +e^x) j.
Compute the integral of C F dot dr if C is the path from (0,0) to (1,0) that follows the spiral r = theta /4pi.

Thank you!
• Nov 29th 2007, 01:31 PM
ThePerfectHacker
Quote:

Originally Posted by universe09
question.

if F(x,y) = f(x,y)i + g(x,y)j
f and g are continuous on an open connected region D.

a) what can you say about the work integrals of F along paths in D if
F = del(phi ), for some function phi(x,y)?

b) what can you say about F and work integral of F along paths in D if fsuby=gsubx throughout D?
What assumptions must be made about D?

For (a) by using the fundamental theorem of line integrals you zero get zero.

For (b) by using Green's theorem you get the integral of 0 over D which is zero.